TR15-054 Authors: Noga Alon, Noam Nisan, Ran Raz, Omri Weinstein

Publication: 7th April 2015 23:53

Downloads: 824

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We continue the study of welfare maximization in unit-demand (matching) markets, in a distributed information model

where agent's valuations are unknown to the central planner, and therefore communication is required to determine an

efficient allocation. Dobzinski, Nisan and Oren (STOC'14) showed that if the market size is $n$, then $r$ rounds of interaction

(with logarithmic bandwidth) suffice to obtain an $n^{1/(r+1)}$-approximation to the optimal social welfare. In particular,

this implies that such markets converge to a stable state (constant approximation) in time logarithmic in the market size.

We obtain the first multi-round lower bound for this setup. We show that even if the allowable per-round bandwidth of each

agent is $n^{\eps(r)}$, the approximation ratio of any $r$-round (randomized) protocol is no better than $\Omega(n^{1/5^{r+1}})$,

implying an $\Omega(\log \log n)$ lower bound on the rate of convergence of the market to equilibrium.

Our construction and technique may be of interest to round-communication tradeoffs in the more general setting of

combinatorial auctions, for which the only known lower bound is for simultaneous ($r=1$) protocols [DNO14].